I have been reading about this and I'm still not sure which one is the best way to take care of the battery.

Once it's full charged, should I unplug it or leave it "charging" instead?

I've read many times that keeping it plugged in kills the battery faster, but I also read that some devices (MacBook pro I think) bring some kind of feature so when it is full charged, it doens't use the battery.

The short answer is that Microsoft suggests you periodically run it down, maybe once a month at minimum. As with most devices run off battery if you leave it plugged in all the time without running it on battery for an extended period the battery won't work as well over time when you actually need it.

Battery careOperating temperature. Surface is designed to work between 32°F and 95°F (or 0°C to 35°C). Lithium-ion batteries are sensitive to high temperatures, so keep your Surface out of the sun and don’t leave it in a hot car.

Recharge any time. The battery doesn’t need to be empty or low before you recharge. You can recharge the battery whenever you like. However, it’s best to let the battery run to below 10 percent at least once per month before you recharge it.

The Surface Batteries are actually some the highest quality batteries in the industry, most Ultrabooks and laptops have between 600-900 cycles, the Batteries in the Surface Devices have between 1500-2100 cycles, the engineering team state that in 3 years a Surface should still have at least 80% capacity under normal use.

I was scared for a minute. Myself and about three dozen users that I support where I work all have their laptops and Surfaces plugged into their docking station or power packs all day long when their in the office. I have never run my battery down intentionally so I guess mine will have a short battery life. It's not a huge concern with me since I rarely am not around electric nor use it all that often on battery.

You can leave it plugged in 29 days a month, but one day a month run the battery down to 10% or 5%. It'll keep it calibrated. But use it as you like! If you go 45 days without unplugging it, it'll be fine, just don't make it a habit to leave it so long plugged in! haha. Mine is probably plugged in 95% of the time, and I intentionally discharge it once a month just to keep it good. My Surface Pro 2, after being used for a full 2 years, has only 200 or so discharges after 700 days of usage! So, it's not bad.